The pilot reported that he approached the turf runway at his home airport with a tailwind, which he estimated to be about 20 knots and gusting. The airplane “just floated” at the intended touchdown point, and then touched down about 1/3 of the way down the 2,500-ft-long runway. After touchdown, the airplane bounced, and he added some engine power “so that the impact of the second touchdown would be mitigated.” After the second touchdown, he applied “maximum braking effort.” He reported that the braking action was “nil” due to the freshly mowed turf, and he was unable to stop the airplane on the runway. The airplane crossed over a road at the end of the runway, nosed over, came to rest inverted, and sustained substantial damage to the vertical stabilizer and rudder. The pilot stated that the opposite runway was not used for landing at this airport, due to tall trees at the approach end, which would have required a touchdown “well past” the midpoint of the runway. Further, the opposite runway had a “radical” downward slope (its elevation decreased about 80 ft over the 2,500-ft length). The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.